毕业设计论文外文文献翻译中英文对照土木工程简要的分析斜坡稳定性的方法

毕业设计论文外文文献翻译中英文对照土木工程简要的分析斜坡稳定性的方法INTERNATIONALJOURNALFORNUMERICALANDANALYTICALMETHODSINGEOMECHANICSInt.J.Numer.Anal.Meth.Geomech.,23,439}449(1999)SHORTCOMMUNICATIONSANALYTICALMETHODFORANALYSISOFSLOPESTABILITYJINGGANGCAOsANDMUSHARRAFM.ZAMAN*tSchoolofCivilEngineeringandEnvironmentalScience,UniversityofOklahoma,Norman,OK73019,U.S.A.SUMMARYAnanalyticalmethodispresentedforanalysisofslopestabilityinvolvingcohesiveandnon-cohesivesoils.Earthquakeeffectsareconsideredinanapproximatemannerintermsofseismiccoe$cient-dependentforces.Twokindsoffailuresurfacesareconsideredinthisstudy:aplanarfailuresurface,andacircularfailuresurface.Theproposedmethodcanbeviewedasanextensionofthemethodofslices,butitprovidesamoreaccurateetreatmentoftheforcesbecausetheyarerepresentedinanintegralform.Thefactorofsafetyisobtainedbyusingtheminimizationtechniqueratherthanbyatrialanderrorapproachusedcommonly.Thefactorsofsafetyobtainedbytheanalyticalmethodarefoundtobeingoodagreementwiththosedeterminedbythelocalminimumfactor-of-safety,Bishop's,andthemethodofslices.Theproposedmethodisstraightforward,easytouse,andlesstime-consuminginlocatingthemostcriticalslipsurfaceandcalculatingtheminimumfactorofsafetyforagivenslope.Copyright(1999)JohnWiley&Sons,Ltd.Keywords:analyticalmethod;slopestability;cohesiveandnon-cohesivesoils;dynamiceffect;planarfailuresurface;circularfailuresurface;minimizationtechnique;factor-of-safety.INTRODUCTIONOneoftheearliestanalyseswhichisstillusedinmanyapplicationsinvolvingearthpressurewasproposedbyCoulombin1773.Hissolutionapproachforearthpressuresagainstretainingwallsusedplaneslidingsurfaces,whichwasextendedtoanalysisofslopesin1820byFrancais.Byabout1840,experiencewithcuttingsandembankmentsforrailwaysandcanalsinEnglandandFrancebegantoshowthatmanyfailuresurfacesinclaywerenotplane,butsigni"cantlycurved.In1916,curvedfailuresurfaceswereagainreportedfromthefailureofquaystructuresinSweden.Inanalyzingthesefailures,cylindricalsurfaceswereusedandtheslidingsoilmasswasdividedintoanumberofverticalslices.TheprocedureisstillsometimesreferredtoastheSwedishmethodofslices.Bymid-1950sfurtherattentionwasgiventothemethodsofanalysisusingcircularandnon-circularslidingsurfaces.Inrecentyears,numericalmethodshavealsobeenusedintheslopestabilityanalysiswiththeunprecedenteddevelopmentofcomputerhardwareandsoftware.OptimizationtechniqueswereusedbyNguyen,10andChenandShao.Whilefiniteelementanalyseshavegreatpotentialformodellingfieldconditionsrealistically,theyusuallyrequiresigni"cante!ortandcostthatmaynotbejusti"edinsomecases.Thepracticeofdividingaslidingmassintoanumberofslicesisstillinuse,anditformsthebasisofmanymodernanalyses.1,9However,mostofthesemethodsusethesumsofthetermsforallsliceswhichmakethecalculationsinvolvedinslopestabilityanalysisarepetitiveandlaboriousprocess.Locatingtheslipsurfacehavingthelowestfactorofsafetyisanimportantpartofanalyzingaslopestabilityproblem.Anumberofcomputertechniqueshavebeendevelopedtoautomateasmuchofthisprocessaspossible.Mostcomputerprogramsusesystematicchangesinthepositionofthecenterofthecircleandthelengthoftheradiustofindthecriticalcircle.Unlesstherearegeologicalcontrolsthatconstraintheslipsurfacetoanoncircularshape,itcanbeassumedwithareasonablecertaintythattheslipsurfaceiscircular.9Spencer(1969)foundthatconsiderationofcircularslipsurfaceswasascriticalaslogarithmicspiralslipsurfacesforallpracticalpurposes.CelestinoandDuncan(1981),andSpencer(1981)foundthat,inanalyseswheretheslipsurfacewasallowedtotakeanyshape,thecriticalslipsurfacefoundbythesearchwasessentiallycircular.Chen(1970),BakerandGarber(1977),andChenandLiumaintainedthatthecriticalslipsurfaceisactuallyalogspiral.ChenandLiu12developedsemi-analyticalsolutionsusingvariationalcalculus,forslopestabilityanalysiswithalogspiralfailuresurfaceinthecoordinatesystem.Earthquakee!ectswereapproximatedintermsofinertiaforces(verticalandhorizontal)definedbythecorrespondingseismiccoe$cients.Althoughthisisoneofthecomprehensiveandusefulmethods,useof/-coordinatesystemmakesthesolutionprocedureattainablebutverycomplicated.Also,thesolutionsareobtainedvianumericalmeansattheend.ChenandLiu12havelistedmanyconstraints,stemmingfromphysicalconsiderationsthatneedtobetakenintoaccountwhenusingtheirapproachinanalyzingaslopestabilityproblem.Thecircularslipsurfacesareemployedforanalysisofclayeyslopes,withintheframeworkofananalyticalapproach,inthisstudy.TheproposedmethodismorestraightforwardandsimplerthanthatdevelopedbyChenandLiu.Earthquakeeffectsareincludedintheanalysisinanapproximatemannerwithinthegeneralframeworkofstaticloading.Itisacknowledgedthatearthquakeeffectsmightbebettermodeledbyincludingaccumulateddisplacementsintheanalysis.Theplanarslipsurfacesareemployedforanalysisofsandyslopes.Aclosed-formexpressionforthefactorofsafetyisdeveloped,whichisdiferentfromthatdevelopedbyDas.STABILITYANALYSISCONDITIONSANDSOILSTRENGTHTherearetwobroadclassesofsoils.Incoarse-grainedcohesionlesssandsandgravels,theshearstrengthisdirectlyproportionaltothestresslevel:''(1),,,,tanf/,f,whereistheshearstressatfailure,theeffectivenormalstressatfailure,/,andtheeffectiveangleofshearingresistanceofsoil.Infine-grainedclaysandsiltyclays,thestrengthdependsonchangesinporewaterpressuresorporewatervolumeswhichtakeplaceduringshearing.Underundrained,uconditions,theshearstrengthcuislargelyindependentofpressure,thatis=0.When''(,)c,drainageispermitted,however,both&cohesive'and&frictional'componentsareobserved.Inthiscasetheshearstrengthisgivenby(2)Considerationoftheshearstrengthsofsoilsunderdrainedandundrainedconditions,andoftheconditionsthatwillcontroldrainageinthefieldareimportanttoincludeinanalysisofslopes.Drainedconditionsareanalyzedintermsofeffectivestresses,using''(,)c,valuesofdeterminedfromdrainedtests,orfromundrainedtestswithporepressuremeasurement.Performingdrainedtriaxialtestsonclaysisfrequentlyimpracticalbecausetherequiredtestingtimecanbetoolong.DirectsheartestsorCUtestswithporepressuremeasurementareoftenusedbecausethetestingtimeisrelativelyshorter.Stabilityanalysisinvolvessolutionofaprobleminvolvingforceand/ormomentequilibrium.Theequilibriumproblemcanbeformulatedintermsof(1)totalunitweightsandboundarywaterpressure;or(2)buoyantunitweightsandseepageforces.Thefirstalternativeisabetterchoice,becauseitismorestraightforward.Althoughitispossible,inprinciple,tousebuoyantunitweightsandseepageforces,thatprocedureisfraughtwithconceptualdiffculties.PLANARFAILURESURFACEFailuresurfacesinhomogeneousorlayerednon-homogeneoussandyslopesareessentiallyplanar.Insomeimportantapplications,planarslidesmaydevelop.Thismayhappeninslope,wherepermeablesoilssuchassandysoilandgravelorsomepermeablesoilswithsomecohesionyetwhoseshearstrengthisprincipallyprovidedbyfrictionexist.Forcohesionlesssandysoils,theplanarfailuresurfacemayhappeninslopeswherestrongplanardiscontinuitiesdevelop,forexampleinthesoilbeneaththegroundsurfaceinnaturalhillsidesorinman-madecuttings.,,,图平面破坏Figure1showsatypicalplanarfailureslope.FromanequilibriumconsiderationoftheslidebodyABCbyaverticalresolutionofforces,theverticalforcesacrossthebaseoftheslidebodymustequaltoweightw.Earthquakeeffectsmaybeapproximatedbyincludingahorizontalaccelerationkgwhichproducesahorizontalforcek=actingthroughthecentroidofthebodyandneglectingverticalinertia.1Forasliceofunitthicknessinthestrikedirection,theresolvedforcesofnormalandtangentialcomponentsNand?canbewrittenas(3)NWk,,(cossin),,(4)TWk,，(sincos),,whereistheinclinationofthefailuresurfaceandwisgivenbyLWxxdxHxdx,,，,,,,,,(tantan)(tan),,0(5)2H,,,(cotcot),,2,whereistheunitweightofsoil,Htheheightofslope,isLHlH,,cot,cot,,,,theinclinationoftheslope.SincethelengthoftheslidesurfaceABis,thecH/sin,resistingforceproducedbycohesioniscH/sina.ThefrictionforceproducedbyNis.Thetotalresistingoranti-slidingforceisthusgivenbyWk(cossin)tan,,,,(6)RWkcH,,，(cossin)tan/sin,,,,Forstability,thedownslopeslideforce?mustnotexceedtheresistingforceRofthebody.Thefactorofsafety,Fs,intheslopecanbedefinedintermsofeffectiveforcebyratioR/T,thatis1tan2,kc,F,，tan(7),skHk，，,tan(sincos)sin(),,,,,,Itcanbeobservedfromequation(7)thatFsisafunctionofa.ThustheminimumvalueofFscanbefoundusingPowell'sminimizationtechnique18fromequation(7).DasreportedasimilarexpressionforFswithk=0,developeddirectlyfromequation(2)F,,,/,byassumingthat,whereistheaverageshearstrengthofthesoil,andsfdf,theaverageshearstressdevelopedalongthepotentialfailuresurface.dForcohesionlesssoilswherec=0,thesafetyfactorcanbereadilywrittenfromequation(7)as1tan,k,(8)F,tan,sk，tan,ItisobviousthattheminimumvalueofFsoccurswhena=b,andthefailurebecomesindependentofslopeheight.Forsuchcases(c=0andk=0),thefactorsofsafetyobtainedfromtheproposedmethodandfromDasareidentical.CIRCULARFAILURESURFACESlidesinmedium-stifclaysareoftendeep-seated,andfailuretakesplacealongcurvedsurfaceswhichcanbecloselyapproximatedintwodimensionsbycircularsurfaces.Figure2showsapotentialcircularslidingsurfaceABintwodimensionswithcentreOandradiusr.Thefirststepintheanalysisistoevaluatethesliding'ordisturbingmomentMsaboutthecentreofthecircleO.Thisshouldincludetheself-weightwoftheslidingmass,andothertermssuchascrestloadingsfromstockpilesorrailways,andwaterpressuresactingexternallytotheslope.Earthquakeeffectsisapproximatedbyincludingahorizontalaccelerationkgwhichproducesahoriazontalforcekd=actingthroughthecentroidofeachsliceandneglectingverticalinertia.WhenthesoilaboveABisjustonthepointofsliding,theaverageshearingresistancewhichisrequiredalongABforlimitingequilibriumisgivenbyequation(2).Theslidemassisdividedintoverticalslices,andatypicalsliceDEFGisshown.Theself-weightofthesliceis.ThemethodassumesthatthedWhdx,,resultantforcesXlandXronDEandFG,respectively,areequalandopposite,andparalleltothebaseofthesliceEF.Itisrealizedthattheseassumptionsarenecessarytokeeptheanalyticalsolutionoftheslopestabilityproblemaddressedinthispaperachievableandsomeoftheseassumptionswouldleadtorestrictionsintermsofapplications(e.g.earthpressureonretainingwalls).However,analyticalsolutionshaveaspecialusefulnessinengineeringpractice,particularlyintermsofobtainingapproximatesolutions.Morerigorousmethods,e.g.finiteelementtechnique,canthenbeusedtopursueadetailsolution.Bishop'srigorousmethod5introducesafurthernumericalproceduretopermitspecialcationofintersliceshearforcesXlandXr.SinceXlandXrareinternalforces,mustbezeroforthewholesection.Resolving()XX,,lrprerpendicularlyandparalleltoEF,onegets(9)Thdxkhdx,，,,,,sincos(10)Nhdxkhdx,,,,,,coscsinxa,22(11),arcsin,rab,,，rTheforceNcanproduceamaximumshearingresistancewhenfailureoccurs:(12)Rcdxhdxk,，,sec(cossin)tan,,,,,TheequationsoflinesAC,CB,andABYaregivenbyy22yxyhybrxa,,,,,,tan,,(),(13)123ThesumsofthedisturbingandresistingmomentsforallslicescanbewrittenaslMrhkdx,，,,,(sincos)s,0ll(14),,，，,，ryykdxryykdx()(sincos)()(sincos),,,,,,1323,,0L,，rIkI(),sclMrchkdx,，,sec(cossin)tan,,,,,,,r,0ll,，,,rcdxryykdxsec()(cossin)tan,,,,,23,,00(15)l，,,ryykdx()(cossin)tan,,,,23,L2,，,rcrIkItan()cs,,,22LHlarbH,,，,,cot,(),(16)laa,(17),arcsinarcsin,，rrLlIyydxyydx,,，,()sin()sin,,1323s,,0L(18)2H1，，2,，,(cot)secabH,,,,23r，，LlIyydxyydx,,，,()cos()cos,,s1323,,0L22tantanbrb,,2222，，,,，,,,，，2()()()rLarLa，，623rr(19)rLara,,,,,，,，,(tan)arcsin(tan)arcsinaHab,,,,,,22rr,,,,rla,1222，，,,，,，,,()arcsin()4()()bHrlablaHa，，26rrThesafetyfactorforthiscaseisusuallyexpressedastheratioofthemaximumavailableresistingmomenttothedisturbingmoment,thatiscrIkI,,,，,tan()McsrF,,(20)sMIkI()，,sscWhentheslopeinclinationexceeds543,allfailuresemergeatthetoeoftheslope,chiscalledtoewhifailure,asshowninFigure2.However,whentheslopeheightHisrelativelylargecomparedwiththeundrainedshearstrengthorwhenahardstratumis0,,3underthetopoftheslopeofclayeysoilwith,theslideemergesfromthefaceoftheslope,whichiscalledFacefailure,asshowninFigure3.ForFacefailure,thesafety()Hh,factorFsisthesameas?oefailure1susinginsteadofH.0Forflatterslopes,failureisdeep-seatedandextendstothehardstratumformingthebaseoftheclaylayer,whichiscalledBasefailure,asshowninFigure4.1,3Followingthesameprocedureasthatfor?oefailure,onecangetthesafetyfactorforBasefailure:''crIkI，,tan(),,,csF,(21)s''IkI，,，，sc''IIwheretisgivenbyequation(17),andandaregivenbysclll01'Iyyxdxyyxdxyyxdx,,，,，,sinsinsin，，，，，，s031323,,,ll000(22)3HHblH222,，,,,,，,，cot()()(2)(33)lllllabbHH,0112223rrrlll01,,,,，，，，，，I,y,ycosd，y,ycosd，y,ycosd,,,xxxc031323ll010(23)Hl1r1,arba,,,,2220,，，,r,Hcot,b,Harcsin,arcsin，,,,,2r42r2r,,,,,HHcot1,,,,222，，，，,,ratan,arcsin，4rl,ab，l,aH,a,,,,,22r6r,,,,22其中，yyxyHybrxa,,,,,,,0,tan,,,(24)，，1231122(25),,,，,，,,,,laHlaHlarbHcot,cot,，，0122Itcanbeobservedfromequations(21)~(25)thatthefactorofsafetyFsforagivenslopeisafunctionoftheparametersaandb.Thus,theminimumvalueofFscanbefoundusingthePowell'sminimizationtechnique.Foragivensinglefunctionfwhichdependsontwoindependentvariables,suchastheproblemunderconsiderationhere,minimizationtechniquesareneededtofindthevalueofthesevariableswhereftakesonaminimumvalue,andthentocalculatethecorrespondingvalueoff.IfonestartsatapointPinanN-dimensionalspace,andproceedfromthereinsomevectordirectionn,thenanyfunctionofNvariablesf(P)canbeminimizedalongthelinenbyone-dimensionalmethods.Differentmethodswilldiferonlybyhow,ateachstage,theychoosethenextdirectionn.Powell"rstdiscoveredadirectionsetmethodwhichproducesNmutuallyconjugatedirections.Unfortunately,aproblemoflineardependencewasobservedinPowell'salgorithm.ThemodiffedPowell'smethodavoidsabuildupoflineardependence.Theclosed-formslopestabilityequation(21)allowstheapplicationofanoptimizationtechniquetolocatethecenteroftheslidingcircle(a,b).TheminimumfactorofsafetyFsminthenobtainedbysubstitutingthevaluesoftheseparametersintoequations(22)~(25)andtheresultsintoequation(21),forabasefailureproblem(Figure4).WhileusingthePowell'smethod,thekeyistospecifysomeinitialvaluesofaandb.Well-assumedinitialvaluesofaandbcanresultinaquickconvergence.Ifthevaluesofaandbaregiveninappropriately,itmayresultinadelayedconvergenceandcertainvalueswouldnotproduceaconvergentsolution.Generally,ashouldbeassumedwithin$?,whilebshouldbeequaltoorgreaterthanH(Figure4).Similarly,equations(16)~(20)couldbeusedtocomputetheFs.minfortoefailure(Figure2)andfacefailure(Figure3),exceptisusedinsteadofHinthecaseoffacefailure.Hh,，，0BesidesthePowellmethod,otheravailableminimizationmethodswerealsotriedinthisstudysuchasdownhillsimplexmethod,conjugategradientmethods,andvariablemetricmethods.ThesemethodsneedmorerigorousorcloserinitialvaluesofaandbtothetargetvaluesthanthePowellmethod.AshortcomputerprogramwasdevelopedusingthePowellmethodtolocatethecenteroftheslidingcircle(a,b)andtofindtheminimumvalueofFs.Thisapproachofslopestabilityanalysisisstraightforwardandsimple.RESULTSANDCOMMENTSThevalidityoftheanalyticalmethodpresentedintheprecedingsectionswasevaluatedusingtwowell-establishedmethodsofslopestabilityanalysis.Thelocalminimumfactor-of-safety(1993)method,withthestateoftheeffectivestressesinaslopedeterminedbythefiniteelementmethodwiththeDrucker-Pragernon-linearstress-strainrelationship,andBishop's(1952)methodwereusedtocomparetheoverallfactorsofsafetywithrespecttotheslipsurfacedeterminedbytheproposedanalyticalmethod.Assumingk=0forcomparisonwiththeresultsobtainedfromthelocalminimumfactor-of-safetyandBishop'smethod,theresultsobtainedfromeachofthosethreemethodsarelistedinTableI.Thecasesarechosenfromthetoefailureinahypotheticalhomogeneousdrysoilslopehavingaunitweightof18.5kN/m3.Twoslopeconfigurationswereanalysed,one1:1slopeandone2:1slope.EachslopeheightHwasarbitrarilychosenas8m.Toevaluatethesensitivityofstrengthparametersonslopestability,cohesionrangingfrom5to30kPaandfrictionanglesrangingfrom103to203wereusedintheanalyses(TableI).Anumberofcriticalcombinationsofcandwerefoundtobeunstableforthemodelslopesstudied.Thefactorsofsafetyobtainedbytheproposedmethodareingoodagreementwiththosedeterminedbythelocalminimumfactor-of-safetyandBishop'smethods,asshowninTableI.Toexaminethee!ectofdynamicforces,theanalyticalmethodischosentoanalyseatoefailureinahomogeneousclayeyslope(Figure2).TheheightoftheslopeHis13.5m;theslopeinclinationbisarctan1/2;theunitweightofthesoilcis17.3kN/m3;thefrictionangleis17.3KN/m;andthecohesioncis57.5kPa.UsingtheconventionalF,2.09methodofslices,LiuobtainedtheminimumsafetyfactorUsingthesminproposedmethod,onecangettheminimumvalueofsafetyfactorfromequation(20)asF,2.08fork=0,whichisveryclosetothevalueobtainedfromtheslicemethod.sminF,1.55,1.37Whenk"0)1,0)15,or0)2,onecanget,and1)23,respectively,whichsminshowsthedynamice!ectontheslopestabilitytobesignificant.CONCLUDINGREMARKSAnanalyticalmethodispresentedforanalysisofslopestabilityinvolvingcohesiveandnoncohesivesoils.Earthquakee!ectsareconsideredinanapproximatemannerintermsofseismiccoe$cient-dependentforces.Twokindsoffailuresurfacesareconsideredinthisstudy:aplanarfailuresurface,andacircularfailuresurface.Threefailureconditionsforcircularfailuresurfacesnamelytoefailure,facefailure,andbasefailureareconsideredforclayeyslopesrestingonahardstratum.Theproposedmethodcanbeviewedasanextensionofthemethodofslices,butitprovidesamoreaccuratetreatmentoftheforcesbecausetheyarerepresentedinanintegralform.Thefactorofsafetyisobtainedbyusingtheminimizationtechniqueratherthanbyatrialanderrorapproachusedcommonly.Thefactorsofsafetyobtainedfromtheproposedmethodareingoodagreementwiththosedeterminedbythelocalminimumfactor-of-safetymethod(finiteelementmethod-basedapproach),theBishopmethod,andthemethodofslices.Acomparisonofthesemethodsshowsthattheproposedanalyticalapproachismorestraightforward,lesstime-consuming,andsimpletouse.Theanalyticalsolutionspresentedheremaybefoundusefulfor(a)validatingresultsobtainedfromotherapproaches,(b)providinginitialestimatesforslopestability,and(c)conductingparametricsensitivityanalysesforvariousgeometricandsoilconditions.REFERENCES1.D.BrunsdenandD.B.Prior.SlopeInstability,Wiley,NewYork,1984.2.B.F.WalkerandR.Fell.SoilSlopeInstabilityandStabilization,Rotterdam,Sydney,1987.3.C.Y.Liu.SoilMechanics,ChinaRailwayPress,Beijing,P.R.China,1990.448SHORTCOMMUNICATIONSCopyright(1999JohnWiley&Sons,Ltd.Int.J.Numer.Anal.Meth.Geomech.,23,439}449(1999)4.L.W.Abramson.SlopeStabilityandStabilizationMethods,Wiley,NewYork,1996.5.A.W.Bishop.&Theuseoftheslipcircleinthestabilityanalysisofslopes',Geotechnique,5,7}17(1955).6.K.E.Petterson.&Theearlyhistoryofcircularslidingsurfaces',Geotechnique,5,275}296(1956).7.G.Lefebvre,J.M.DuncanandE.L.Wilson.&Three-dimensional"niteelementanalysisofdams,'J.SoilMech.Found,ASCE,99(7),495}507(1973).8.Y.KohgoandT.Yamashita,&Finiteelementanalysisof"lltypedams*stabilityduringconstructionbyusingthee!ectivestressconcept',Proc.Conf.Numer.Meth.inGeomech.,ASCE,Vol.98(7),1998,pp.653}665.9.J.M.Duncan.&Stateoftheart:limitequilibriumand"nite-elementanalysisofslopes',J.Geotech.Engng.ASCE,122(7),577}596(1996).10.V.U.Nguyen.&Determinationofcriticalslopefailuresurface',J.Geotech.Engng.ASCE,111(2),238}250(1985).11.Z.ChenandC.Shao.&Evaluationofminimumfactorofsafetyinslopestabilityanalysis,'Can.Geotech.J.,20(1),104}119(1988).12.W.F.ChenandX.L.Liu.?imitAnalysisinSoilMechanics,Elsevier,NewYork,1990.13.N.M.Newmark.&E!ectsofearthquakesondamsandembankments',Geotechnique,15,139}160(1965).14.B.M.Das.PrinciplesofGeotechnicalEngineering,PWSPublishingCompany,Boston,1994.15.A.W.SkemptonandH.Q.Golder.&Practicalexamplesofthe/"0analysisofstabilityofclays',Proc.2ndInt.Conf.SMFE,Rotterdam,Vol.2,1948,pp.63}70.16.L.Bjerrum,andT.C.Kenney.&E!ectofstructureontheshearbehaviorofnormallyconsolidatedquickclays',Proc.Geotech.Conf.,Oslo,Norway,vol.2,1967,pp.19}27.17.A.W.Skempton,&Long-termstabilityofclayslopes,'Geotechnique,14,77}102(1964).18.D.G.Liu,J.G.Fei,Y.J.YuandG.Y.Li.FOR?RANProgramming,NationalDefenseIndustryPress,Beijing,P.R.China,1988.19.W.H.Press,B.P.Flannery,S.A.TeukolskyandW.T.Vetterling,NumericalRecipes:?heArtofScienti,cComputing,CambridgeUniversityPress,Cambridge,1995.20.M.G.AndersonandK.S.Richards.SlopeStability:GeotechnicalEngineeringandGeomorphology,Wiley,NewYork,1987.21.R.Baker.&Determinationofcriticalslipsurfaceinslopestabilitycomputations',Int.J.Numer.Anal.Meth.Geomech.,4,333}359(1980).22.A.K.Chugh.&Variablefactorofsafetyinslopestabilityanalysis',Geotechnique,?ondon,36(1),57}64(1986).23.B.M.Das.PrinciplesofSoilDynamics,PWS-KentPublishingCompany,Boston,1993.24.S.L.HuangandK.Yamasaki.&Slopefailureanalysisusinglocalminimumfactor-of-safetyapproach',J.Geotech.Engng.ASCE,119(12),1974}1987(1993).25.S.L.Kramer.GeotechnicalEarthquakeEngineering,PrenticeHall,EnglewoodCli!s,NJ,1996.26.D.LeshchinskyandC.Huang.&Generalizedthreedimensionalslopestabilityanalysis',J.Geotech.Engng.ASCE,118(11),1748}1764(1992).27.K.S.LiandW.White.&Rapidevaluationofthecriticalsurfaceinslopestabilityproblems',Int.J.Numer.Anal.Meth.Geomech.,11(5),449}473(1987).28.D.W.Taylor.FundamentalsofSoilMechanics,Wiley,Toronto,1948.29.U.S.FederalHighwayAdministration,Advanced?echnologyforSoilSlopeStability,U.S.Dept.ofTransportation,Washington,DC,1994.30.Spencer(1969).31.CelestinoandDuncan(1981).32.Spencer(1981).33.Chen(1970).34.BakerandGarber(1977).35.Bishop(1952).简要的分析斜坡稳定性的方法JINGGANGCAOs和MUSHARRAFM.ZAMAN诺曼底的俄克拉荷马大学土木环境工程学院摘要本文给出了解析法对边坡的稳定性分析,包括粘性和混凝土支撑。地震被认为是用和振动相似的方式产生的地震从属效应。这篇论文涉及到了两种破坏面:一个平面的破坏面,一个圆形的破坏面，这个合适的方法可以被视为切割方法的延伸，但是它提供了更加精确的计算力的方法，因为他采用的是积分的方法。安全的方法是利用最小化的技术,而不是一般的由一个反复的试验方法。安全的因素所获得的分析方法是符合最初最低基本安全因素的方法—切割法。推荐的方法是基于最危险滑动面的直接的，最简单的去用并且最快的计算，和计算该斜坡的最小安全系数。关键词:解析方法;岩质边坡稳定性;有粘性和无粘性土;动力学因素;平坦的破坏面;圆形破坏面;估算最小值的方法;影响安全性的因素介绍最早的用在分析土应力的方法被认为是库伦在1773年提出来的。他的解决挡土墙土应力的方法用的是滑动面，在1820年法国这个被延伸用来分析边坡。直到1840年，英国和法国的铁路和隧道的钻凿和路堤经验表明了许多泥土中的破坏面不是平的，而是没有规律的弯曲的。1916年，不规则的破坏面在码头结构破坏中出现在瑞典。分析了这些破坏面之后，圆柱体截面被采用，并且滑移土体被分成了一定数量的条形体。这个解决程序有时候也被称为“瑞典条分法”。到十九世纪五十年代中期，人们的注意力转移到了用圆形和非圆形滑动面的分析上了。近些年来，随着电脑的硬件和软件史无前例的发展，数值分析法已经被用在了边坡稳定性分析上。最好的方法是Nguyen,andChenandShao用的，当有限元分析有模拟真实的土质情况的时候，他们一直需要巨大的人力和物理，这些可能是没有结果的。这个方法的滑动到数片仍然在被使用,它形成了许多现代分析基础,然而,大多数的这些方法的使用条款所有切片使计算边坡稳定性分析中所涉及的重复性和艰苦的过程。定位的滑动面具有最低的安全系数的分析,是一个边坡稳定问题重要的一部分。大量的计算机技术已经发展到自动化许多这样的过程。大多数的计算机程序在中心的位置,利用半径的长度使用系统的变化找到临界圆。除非有地质控制去约防止动面称为一个圆形状,它可以被认为是某一个合理的圆形边坡。承担合理的滑动面是circular.9斯潘塞(1969)发现考虑的圆形滑移面和对数螺旋滑动面是同样临界的使用目的。Celestino和邓肯(1981年)、斯潘塞(1981年)的研究发现,在分析滑动面形状可以发生任何变形的地方滑动面被证明基本上都是圆形的。陈(1970),贝克和Garber(1977年)、陈、Liu12坚持滑动面实际上是一个切削螺旋型的。为解决边坡稳定性分析，陈和Liu12发表的解析在坐标系里是利用,,变分微积分,和对数螺旋线破裂面的来分析的。地应力是几乎按照地震系数定义,,的惯性力来估计的。虽然利用坐标系来解决方案是一个综合的测验和有用的方,,法,但是这种方法是十分复杂的。同时,采用数值方法最后也能解决问题。陈和刘列出了对边坡稳定性分析时需要考虑的很多,出于物理因素的限制。在此研究中圆形滑动面是用于粘土质斜坡分析框架内的一个。分析方法。所提出的方法比陈和刘提出的方法更直接、更简单地震效应也包含在相似的总体框架相对静载的方法中。地震效应可以在位移模拟的分析方法中被更好的模拟是公认的。平缓的滑动面用来分析砂性的斜坡。一个安全系数的解析表达式发展并且被应用了，这是不同于Das所提出的分析方法的。稳定性分析条件和土壤应力有两种级别的土壤。在无粘性土和砂石中，剪切力是和应力成正比的:''(1),,,,tanf//,f,,是破坏时的剪切力，是破坏时的正应力，是土壤的摩擦角。在粉质粘土和细粘土中，应力取决于孔隙水压力或者是水在剪切过程中占cu得体积。在没有排水措施的前提下，剪切力很大程度上是和压力无关的，也就,''u(,)c,是说=0.当有排水设施时，不管是密实的或者是有摩擦的，他们的系数都是遵循上述规律的。这种情况下，剪切强度如下式:考虑到剪力强度在排水和不排水条件下的不同，所以排水情况在边坡分析中是非常重要的。排水条件是依据应力值确定的，用的是排水和不排水条件下的孔隙压''(,)c,力测试来确定系数的。对粘土采用三周压缩试验的排水方法通常是不合适的，因为所需要的测试时间可太长了。经常采用直剪试验或CU测试孔隙水压力是因为测试时间是相对较短的。稳定性分析包括解决涉及力和力矩平衡的问题。公式(1)利用容重和水压力界限可以来解决平衡问题，或者通过公式(2)利用浮容重和渗流压力。第一个方案是比较好的选择，是因为他更加直接，他的步骤只是存在概念上的不同。二维破坏面均匀的或者是不均匀的砂性边坡的破裂面是二维的。在一些重要的二维滑坡的应用是可以应用的。这种方法可以用在可渗透性的土壤，比如砂性土和砾石，或者是有内聚力的砂性土，这种土的剪切力是由摩擦力提供的。对于无粘性的砂性土，边坡的二维破坏面可能发生在较大的二维间断点发育的地方，比如在自然或者是人工的山体土壤的下面是自然的土质中。,,,图平面破坏图1显示一典型的平面失败的斜坡。把滑动体ABC上的平衡力竖向分解，作用在滑动体上的垂直力一定是平衡与滑动体的自重W的。振动力是接近包括同一水平线上的重力加速度，它产生了一个水平方向的作用在滑动体重心上的力KW，并且不考虑竖直方向的惯性。对于作用力方向的一个单位层厚度，已知常力及其分量N、T可以按下式:(3)NWk,,(cossin),,(4)TWk,，(sincos),,其中为破坏面的倾斜角，W按照下式计算:LWxxdxHxdx,,，,,,,,,(tantan)(tan),,0(5)2H,,,(cotcot),,2,式中，是土壤的容重，H是边坡的高，，是边坡的LHlH,,cot,cot,,,,倾斜。滑动面长AB为，摩擦阻力为，N产生的摩擦力是H/sin,cH/sin,，总的抗滑力按下式给出:Wk(cossin)tan,,,,(6)RWkcH,,，(cossin)t